Nitrogen gas is filled in an insulated container. If $\alpha$ fraction of moles dissociates without exchange of any energy,then the fractional change in its temperature is ..............

Read the given statements and decide which is/are correct on the basis of the kinetic theory of gases:
$(I)$ Energy of one molecule at absolute temperature $T = 0 \ K$ is zero.
$(II)$ $r.m.s.$ speeds of different gases are the same at the same temperature.
$(III)$ For one gram of all ideal gases,kinetic energy is the same at the same temperature.
$(IV)$ For one mole of all ideal gases,mean kinetic energy is the same at the same temperature.

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 = \text{constant}$. The coefficient of volume expansion of the gas is . . . . . . .

At a temperature of $300 \ K$,the average translational kinetic energy and $rms$ speed of a sample of oxygen gas are $6.21 \times 10^{-21} \ J$ and $484 \ m/s$ respectively. At $600 \ K$,these values will be respectively: (Assume ideal gas behavior)

What is/are the same for $O_2$ and $NH_3$ in gaseous state?

An insulated container containing a monoatomic gas of molar mass $M$ is moving with a velocity $V_{0}$. If the container is suddenly stopped,find the change in temperature.